On the Kramers Very Low Damping Escape Rate for Point Particles and Classical Spins
Résumé
This chapter demonstrates in didactic fashion how both the very low dissipation (VLD) escape rate for point particles with separable and additive Hamiltonians and the corresponding rate for giant classical spins where the Hamiltonian is nonseparable and nonadditive may be simply obtained by using the Stratonovich treatment based on the Langevin equation with multiplicative noise. It first presents a very brief introduction to the escape rate problem as envisaged by Kramers. It then explains the work of Arrhenius who, from a study of experimental data, viewed a chemical reaction as very few particles from a huge assembly in a well escaping over a potential barrier. The chapter also discusses the energy-controlled diffusion of point particles with separable and additive Hamiltonians. Finally, it considers the motion of a lightly damped particle librating in the potential V(x) in the absence of the stochastic noise term.